My plan is to stick the Nuvo Boehm headjoint on a 19mm ID PVC body with fingerholes placed like a Low D Whistle and see what happens. What I hope happens is a thing that plays sort of like a flute but is played vertically like a whistle.

Contact me before you start drilling any holes ... I may be able to help you reduce the number of failed experiments. Because of differences in sound-generation mechanism, and the headspace between cork and embouchure hole on the headjoint, you can't put the holes exactly where they'd go for a low whistle.

I would have thought that whatever is used to generate a tone, the division of the tube to create the scale would be similar.

What I was planning to do was, before I drilled any holes, stick the headjoint on the body of a Low D with the same ID as the PVC pipe and see what sort of scale resulted. But if you have a known formula that would be great.

Not a formula ... a computer program. It builds a detailed model of the acoustics of the whole instrument. It works best when calibrated to a real mouthpiece, and the experiment with the low D body that you describe is the best way to calibrate it. This page describes the tuning information I'd be asking you for; I'd prefer actual frequencies (in Hertz), but I can work with descriptions like "45 cents flat of low E" if necessary.

I'd also be asking for measurements of the body and the headjoint: bore sizes, how far down the holes are and how big they are, that sort of thing. With the curves in the headjoint, I'd have to settle for an approximation of how far up the embouchure hole is from the bottom.

A lot of numbers, but with those numbers the program can give us a good idea what the flute body would have to look like to play in tune.

Well yesterday I made a quick-and-dirty Irish Low D Quenacho out of Schedule 40 3/4" PVC pipe, which has an ID of 19mm, similar to a Boehm C flute. I think it took a half hour total.

I cut a notch on one end of a long length of the pipe. I sawed off the bottom of the tube to where I thought I'd get a D, based on a Low D whistle (hit it on the first try, whew). Then I laid the Low D Whistle aside my creation, marked the hole positions, and drilled. Surprisingly the thing plays in tune fairly well; some of the holes need to be carved out due to being a bit flat, but happily none are too sharp.

This time the octaves are good, don't know why.

The notch is pretty small. I'll try enlarging it bit by bit until it gets worse, then start over I suppose.

My low D came in last week ad I've been having a lot of fun with it! There's quite a learning curve on the kena style mouthpiece, and I think it's probably way more like a flute than a whistle. I'm enjoying the range of tones I can get depending on my embouchure, but I'm not a fan of how easy it is to bump the instrument and lose the embouchure altogether. This will doubtless improve with practice.

I played the lower and upper D with a tuner app and both were +/- 5 cents of true, which is better than I've been able to get with any of my whistles.

I find it works best for me at least if I use piper's grip with both hands, and I'm glad I ordered the Becker low D first so I could learn the grip on a lighter whistle.

I am not a good enough player to be able to say one way or another how responsive it is to various ornaments.

Overall, I thoroughly endorse this thing! I never know what to call it though, since "Open Whistle" means nothing to most people. "Irish Kena?" "Hybrid Whistle?" Eh.